Ballistic transport in graphene grown by chemical vapor deposition

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by  V. E. Calado

Ballistic transport in graphene grown by chemical vapor deposition
V. E. Calado,1,a) Shou-En Zhu,2,a) S. Goswami,1 Q. Xu,1 K. Watanabe,3 T. Taniguchi,3 G. C. A. M. Janssen,2
and L. M. K. Vandersypen1,b)
1)Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft,
The Netherlands
2)Micro and Nano Engineering Laboratory, Precision and Microsystems Engineering, Delft University of Technology,
2628 CD Delft, The Netherlands
3)Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044,
Japan
In this letter we report the observation of ballistic transport on micron length scales in graphene synthesised
by chemical vapour deposition (CVD). Transport measurements were done on Hall bar geometries in a liquid
Hecryostat. Usingnon-localmeasurementsweshowthatelectronscanbeballisticallydirectedbyamagnetic
field (transverse magnetic focussing) over length scales of ∼1 µm. Comparison with atomic force microscope
measurements suggests a correlation between the absence of wrinkles and the presence of ballistic transport
in CVD graphene.
4
1
0 High electronic quality in graphene is a key require-
(a)
2 ment for many experiments and future applications1.
n The highest quality has so far been achieved in ex-
a foliated graphene2, either by suspending the graphene
J flakes3 orbydepositingthemonhexagonalboronnitride

7 (hBN)substrates4. Tomovebeyondalaboratorysetting,
2 mass production of graphene is essential. Among several

promising synthesis methods, chemical vapor deposition
]
l (CVD)isalow-cost,scalableandcontrollablemethodfor
l
a the production of monolayer graphene5,6. Using CVD,
h large and predominantly monolayer graphene of high 0.5 mm
- quality has been synthesized on copper foils7. Consid-
s
e erable effort has been made to scale up the technology (b) (c)
2D
m to produce meter-sized foils8,9 and to achieve crystals
t. with∼mmdimensions10–12. Suchlargecrystalsizesmin- a.u.)
a imize short-range scattering from grain boundaries13–16. y (
m Also for CVD graphene, the highest electronic quality is nsit G
e
- realized by transferring it onto hBN17,18, using a clean nt
d (contaminant-free) and dry procedure4,19. I
n
Despite this effort the electronic quality of CVD 50 μm
o
graphene is still considered to be inferior to that of ex- 1200 2000 2800
c
[ foliated graphene, and, in particular, there are no re- Raman shift (cm-1)
portsofballistictransportphenomenainCVDgraphene.
1 Ballistic transport is of relevance for realizing elec- FIG. 1. (a) Scanning electron microscope (SEM) image of
v tron optics experiments such as Veselago lensing20 and a copper foil with isolated graphene crystals after a short
1 growth time. (b) An SEM image of one of the crystals in
7 angle-resolved Klein tunnelling21 or specular Andreev (a), where the dendritic shape at the edges is visible. The
7 reflection22. A negative bend resistance in a cross
dark stripes are different crystal orientations in the Cu. (c)
6 geometry23,24 gives a first indication of ballistic trans-
Ramanspectrumtakenofanothergrapheneflaketransferred
1. port. A more sensitive probe, since it is more eas- from copper to SiO2, grown in similar conditions. Inset: a
0 ily affected by small angle scattering, is transverse typicaldiffractionpattern,recordedinatransmissionelectron
4 magnetic focussing (TMF), seen two decades ago in a microscope (TEM).
1 GaAs/AlGaAs 2-dimensional electron gas25 and only re-
: cently in exfoliated graphene26.
v
Xi Here we report ballistic transport in graphene grown port is demonstrated in the form of transverse magnetic
by the CVD method. Large grain size single crystals
focussing (TMF).
r are grown on a folded copper foil enclosure and subse-
a Following the work of Refs.7,10, a copper foil with a
quently dry-transferred onto hBN flakes. Ballistic trans-
thickness of 25 µm is cut in ∼ 2×3 cm2 sheets (Alfa
Aesar > 99.8% pure). The foil is folded to form a fully
enclosedpocketandplacedinsideaquartztubeinahome
a)Contributedequallytothiswork built tube oven. 0.5 sccm CH and 2 sccm H is fed
4 2
b)Electronicmail: [email protected] throughthetubewithaCH partialpressureoflessthan
4
2
20 µbar. The temperature is set to 1050 ◦C, close to the (a) device (c) Carrier density (1011 cm-2)
-6 -4 -2 0 2 4 6
Cu melting point. With these parameters we obtain a
4
lFoiwg.n1uaclweaetisohnowdeanssitcyaninnitnhgeeilnescitdreonofmthicerofosicloppoeck(SetE.MIn) gate gate e (kΩ) 3 L1 F4RiKTt
image of seven graphene crystals on copper spread over c
oafn∼are1a.1ofm3m.1−×2.2.0Wmitmh2s.uTchhiasyloiweldnsuaclneuactiloeantidoenndsietnysiwtye Cr/Au hBN 25 μm esistan 2 L4
are able to grow crystals that have an average diameter (b) graphene Cr/Au heet r 1
of ∼ 1 mm. However, in this letter we used isolated hBN S
crystals, formed in the early stage of CVD growth, such Gate 0
-8 -4 0 4 8
as the one shown in Fig. 1b. These crystals are about SiO2 / Si Gate voltage (V)
150 µm across and are grown in about 30 min. The
crystals have a sixfold dendritic shape. We note that at FIG. 2. (a) Optical microscope image of the device. A hBN
the nucleation site, a second layer starts growing. flake (light blue) is transferred onto a tungsten bottom gate.
In Fig. 1c we show a Raman spectrum taken on a Yellow stripes are the gold contacts. They are deposited in
twosteps,withtheouterpartmuchthicker(∼350nm)than
graphene crystal similar to those in Fig. 1a, after trans-
the inner part, leading to the circular pattern in the image.
fer to SiO . The spectrum confirms that the crystals are
2 (b) A schematic side view of the device, with the materials
monolayer graphene27 with a defect density below the
indicated. The hBN acts here as a dielectric between the
Raman detection limit, as no D line at ∼ 1350 cm−1
graphene and W bottom gate. (c) Black and cyan: the sheet
is visible. In the inset of Fig. 1c a transmission elec-
resistance as a function of gate voltage and carrier density
tron microscope (TEM) diffraction pattern is shown. It taken at 4 K respectively room temperature between probes
confirms a hexagonal lattice28. We have recorded many L and L (see inset). Red: a fit to the 4K data using the
1 4
more diffraction patterns29, which show the same lattice self-consistent equation for diffusive transport as a model.
orientation over a distance of ∼ 50 µm. This indicates
that the graphene patches in Fig. 1a and Fig. 1b are
monocrystalline, i.e. have no grain boundaries. CVD
graphene on copper is transferred onto a hBN flake29. where µc is the mobility from long range scattering, σ0
the minimum conductivity at the CNP and ρ the resis-
The hBN flakes are prepared by mechanical exfoliation s
tivity from short range scattering. This model fits very
on a polymer substrate. A 250 nm thick hBN is selected
andtransferredbythemethoddescribedinRef.19ontoe- well to the data when we account for the electron-hole
asymmetry by using different fit parameters for the two
beam defined tungsten (W) gate electrodes, so that the
sides. For the low temperature hole mobility we find
hBN acts as a gate dielectric. The tungsten can with-
stand high temperatures (∼ 600 ◦C) during annealing µh =41500±800cm2 V−1 s−1,fortheelectronmobility
µ = 28700±600 cm2 V−1 s−1. The RT mobilities are
to remove residues from the hBN flake. Furthermore e
about a factor two lower29.
the bottom gate screens charged impurities, presumably
present in the SiO below. For the resistivity from short range scattering we ob-
2
We have contacted the CVD graphene flake with e- tain ρS = 280±10 Ω for holes and ρS = 380±10 Ω for
beam lithography defined 3 nm Cr / 25 nm Au contacts electrons. These are higher than what has been found
(Fig. 2a) and subsequently etched Hall bars with reac- earlier for exfoliated flakes on hBN (∼ 70 Ω)4. For the
tive ion etching in oxygen. In Fig. 2b we give a device residual conductivity σ0 we find a value of 221±1.5 µS,
schematic. whichis5.70±0.04e2/h. Themobilityvaluesfoundhere
Transport measurements were done in vacuum at 4 K areforlongrangescatteringonly. UsingtheDrudemodel
and at room temperature (RT). In Fig. 2c we show the ofconductivityonefindsameanfreepathof200−400nm
sheet resistance measured at 4 K in black and at RT for a density of 7·1011 cm−2.
in cyan. The resistance peak at the charge neutrality Next, we test whether this device allows transverse
point (CNP) became taller and narrower upon cooling magnetic focusing (TMF). The observation of TMF
as expected. We applied a 1 µA dc current bias across woulddirectlyimplytheoccurrenceofballistictransport
the Hall bar (in the inset) and measured the voltage be- inthatpartofthedevice. AsshownintheinsetofFig.3,
tween terminals L1 and L4 as a function of gate volt- we apply a magnetic field perpendicular to the device
age on the tungsten bottom gate. The charge carrier with a current bias from contact L to R . The Lorentz
2 2
density is tuned by the gate voltage with a coupling force will act on the charge carriers and will steer them
strength of 7.45±0.02·1010 cm−2 V−1, extracted from in a circular orbit with cyclotron radius R = ¯hk /eB,
c F
Hall measurements29. We find the CNP is offset by only where R is the cyclotron radius. Electrons leaving con-
c
3.31·1010cm−2,indicatingverylittlebackgrounddoping. tact L can reach contact L when the cyclotron radius
2 3
We characterize the transport properties of the device matches one half the distance between the contacts L,
by fitting the 4K data with the self-consistent Boltz- provided the electrons are not scattered while traveling
mann equation for diffusive transport that includes long alongthesemi-circlejoiningthecontacts. Thisfocussing
and short range scattering30,31: ρ=(neµ +σ )−1+ρ , condition occurs for specific combinations of magnetic
c 0 S
3
tion of magnetic field and gate voltage, giving rise to a
A 101 102 103 104V/I (Ω) sharp peak in the plot, illustrates the sensitivity of the
L R bias
1 1 focussingeffecttoscattering: onlysmalldeviationsaway
L I
L bias R from the proper semi-circular path are enough to make
20 2 2 15
electrons miss contact L .
L R 3
3 3 From a fit to the data, we find a distance of L =
10
10 L4 B R4 -2m) 570 nm, which corresponds to a semicircle distance of ∼
900nmthatelectronshavetravelled. Thisvalueissome-
c
oltage (V) 0 V B 05 11nsity (10 w5ta0hc0attnsmelap.ragAreartsitiomhnainlfarrothmmeiTesmxMpaFetcctahendbdeltitthwheeoelginrtahtpohhgericeaxpdthirsiactcadtneicsdet2ac9noncoe-f
e v de was recently reported in exfoliated graphene26. In these
Gat-10 -5 Carrier etixppleesriomfetnhtes,BTvMalFuepgeiavkesnwinerEeqs.ee1n. Talhseoaabtsienntceegeorfmsuuclh-
-10 peaksinourmeasurementssuggeststhattheedgesinour
samplearetooroughordirtytoallowspecularreflection.
-20 -15 Wehaveperformedanalogousmeasurementsacrossthe
entire device and except between L and L no focussing
1 2
-5 -4 -3 -2 -1 0 1 2 was found in other parts29, pointing at the presence of
Magnetic field (T) inhomogeneities. IntheinsetofFig.3weshowanatomic
force microscope (AFM) image of the device. In the de-
FIG. 3. The resistance V/I as function of gate voltage vice a bubble and two wrinkles are present, which may
bias
and magnetic field plotted in a logarithmic color scale. The hindertransport. Thewrinklesare1−2nminheightand
straightlinesareduetoSdHoscillationsandthesquare-root less than ∼40 nm in width (not accounting for convolu-
line is due to TMF, indicated by arrows. Inset: AFM image
tion with the AFM tip width). The bubbles are about
of the measured device, showing the non-local measurement
∼35nmhigh. Theapparentconnectionbetweentheab-
configuration used for observing magnetic focussing. V is
senceofwrinklesorbubblesandtheobservationofTMF
measured between L and B while a current bias is applied
3 in this device indicates that is worth investigating more
between L and R .
2 2
systematically whether such wrinkles and bubbles are
sufficient to spoil ballistic effects. More measurements
field and gate voltage: and further discussion of the inhomogeneity of the de-
vice is found in Ref.29. We note that given the presence
B = 2¯hkF ∝(cid:112)V . (1) of the wrinkles and bubbles in the Hall bar, the mobility
eL gate values are remarkably high, in the range of the highest
reported mobilities in CVD graphene17.
The momentum of the charges, h¯k , is tuned with the
F
bottom gate voltage V . In summary, we have demonstrated that TMF can be
gate
When electrons reach contact L , its potential will be observed in CVD graphene on a micron scale distance.
3
raised. We probe this potential by recording the voltage The CVD process was optimized to obtain large single
V between terminal L and B, making the assumption crystal flakes. In order to preserve its high quality we
3
thatthepotentialofthefar-awaycontactBremainscon- havetransferredgrapheneflakeswithadrymethodonto
stant. Thegatevoltageandmagneticfieldaresweptand hBN. The main limitation in electronic quality for the
the resistance V/I is plotted on a logarithmic color- current device appears to be the presence of wrinkles
bias
scale in Fig. 3. and bubbles. If one optimizes further the processing to
In Fig. 3, above fields of ±1 T Shubnikov-de Haas reduce or eliminate the wrinkles and bubbles, it may
(SdH) oscillations are seen as straight lines diverging for becomepossibletoroutinelyobserveballisticphenomena
larger magnetic field. However the lines marked with in CVD graphene. Already, the present results are an
white arrows do not fit the SdH pattern. These lines are import step forward in the direction of scalable and
attributed to TMF, following from the square-root de- controllable graphene production not only for industrial
pendence between the magnetic field and charge carrier applications but also for fundamental research involving
density, see Eq. 1. For negative field and positive gate ballistic effects in graphene.
voltage, electrons leaving L are deflected towards con-
2
tact L , where an increase of the voltage V is observed. We thank A.M. Goossens for discussions and
3
For positive field and negative gate voltage, we find the R. Schouten, R. Luttjeboer, P. van Holst, H. Jansen,
same square-root dependence, where holes are deflected L. Schipperheijn for technical assistance. We thank
instead of electrons. Such behavior canonly be observed G.F. Schneider and S.R.K. Malladi for preparing the
when the region between the contacts permits ballistic TEM sample and H. Zandbergen for providing access to
transport, i.e. little scattering takes place. The fact that the TEM setup. We acknowledge the Young Wild Idea
the focussing signal appears only for a specific combina- Grant from the Delft Centre for Materials (DCMat) for
4
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